Phyrexian mana is not a new color. Players can't produce Phyrexian mana.

To calculate the mana value of a card with Phyrexian mana symbols in its cost, count each Phyrexian mana symbol as 1.

As you cast a spell or activate an activated ability with one or more Phyrexian mana symbols in its cost, you choose how to pay for each Phyrexian mana symbol at the same time you would choose modes or choose a value for X.

A card with Phyrexian mana symbols in its mana cost is each color that appears in that mana cost, regardless of how that cost may have been paid.

If you're at 1 life or less, you can't pay 2 life.

If a permanent ever has both +1/+1 counters and -1/-1 counters on it at the same time, they're removed in pairs as a state-based action so that the permanent has only one of those kinds of counters on it.

An ability that triggers "Whenever you proliferate" triggers even if you chose no permanents or players while doing so.

If a player or permanent has more than one kind of counter on it, and you choose for it to get additional counters, it must get one of each kind of counter it already has. You can't have it get just one kind of counter it already has and not the others.

Players can respond to a spell or ability whose effect includes proliferating. Once that spell or ability starts to resolve, however, and its controller chooses which permanents and players will get new counters, it's too late for anyone to respond.

To proliferate, you can choose any permanent that has a counter, including ones controlled by opponents. You can choose any player who has a counter, including opponents. You can't choose cards in any zone other than the battlefield, even if they have counters on them.

You don't have to choose every permanent or player that has a counter, only the ones you want to add another counter to. Since "any number" includes zero, you don't have to choose any permanents at all, and you don't have to choose any players at all.